A Lower Bound on the Expected Distortion of Joint Source-Channel Coding

Yuval Kochman; Or Ordentlich; Yury Polyanskiy

doi:https://doi.org/10.1109/ISIT.2019.8849390

A Lower Bound on the Expected Distortion of Joint Source-Channel Coding

Yuval Kochman, Or Ordentlich, Yury Polyanskiy

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of blocklength n. Our main result is that in general the convergence rate is not faster than n^-1/2. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least Ω(n^-1/2) above the asymptotic value, if the "bandwidth expansion ratio" is above 1.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1332-1336
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849390
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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https://doi.org/10.1109/ISIT.2019.8849390

Cite this

Kochman, Y., Ordentlich, O., & Polyanskiy, Y. (2019). A Lower Bound on the Expected Distortion of Joint Source-Channel Coding. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1332-1336). Article 8849390 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849390

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Kochman, Y , Ordentlich, O & Polyanskiy, Y 2019, A Lower Bound on the Expected Distortion of Joint Source-Channel Coding. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849390, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 1332-1336, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849390

A Lower Bound on the Expected Distortion of Joint Source-Channel Coding. / Kochman, Yuval ; Ordentlich, Or; Polyanskiy, Yury.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1332-1336 8849390 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of blocklength n. Our main result is that in general the convergence rate is not faster than n-1/2. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least Ω(n-1/2) above the asymptotic value, if the "bandwidth expansion ratio" is above 1.

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Kochman Y , Ordentlich O, Polyanskiy Y. A Lower Bound on the Expected Distortion of Joint Source-Channel Coding. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1332-1336. 8849390. (IEEE International Symposium on Information Theory - Proceedings). doi: https://doi.org/10.1109/ISIT.2019.8849390

A Lower Bound on the Expected Distortion of Joint Source-Channel Coding

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